Name: sizing beams for safe bending loads
Uploaded: 2024-05-23T12:59:46.000Z
Duration: 1 min 23 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Physics

PHYS.2

PHYS.2.D

Design of Prismatic Beams for Bending

תהליך התכנון של קורות פריזמטיות הנתונות לכיפוף מתחיל בקביעת הלחץ המותר לחומר הנבחר.
הלחץ המותר מתקבל בדרך כלל מטבלה של תכונות חומר או מפרט עיצוב. לחלופין, ניתן לחשב אותו על ידי חלוקת החוזק הסופי של החומר על ידי גורם בטיחות מתאים.
לאחר מכן, כוח הגזירה ודיאגרמות רגע הכיפוף המתאימות לתנאי הטעינה שצוינו מצוירים.
לאחר מכן, הערך המוחלט המרבי של רגע הכיפוף מחושב באמצעות דיאגרמת כוח הגזירה.
לאחר מכן מחושב מודולוס החתך המינימלי המותר באמצעות ערך מומנט הכיפוף המוחלט של הקרן והמתח המותר.
כאשר מתכננים קורת עץ, בדרך כלל מצוין היחס המאפיין את צורת חתך הרוחב שלה. הממדים הלא ידועים מזוהים באמצעות היחס בין מידות הקרן לבין מודולוס הקטע.
בעת תכנון קורת פלדה מגולגלת, מתייחסים לטבלה המכילה תכונות של קורת הפלדה המגולגלת, ומתייחסים רק לקטעי הקורה עם מודולוס חתך גדול או שווה למודולוס החתך המינימלי הנדרש.

עיצוב קורות מנסרתיות לכיפוף

<div style="direction: rtl;">
 התכנון של קורות מנסרה, אלמנטים מבניים בעלי חתך אחיד, מתמקד בהבטחת בטיחות ושלמות מבנית תחת עומס. תהליך התכנון מתחיל בקביעת המתח המותר, בין אם מתוך טבלאות מאפייני החומר, או על ידי חלוקת החוזק הסופי של החומר בגורם בטיחותי. מקדם בטיחות זה חיוני לעמידה באי-ודאויות, ומשתנה בהתאם לחומר - עץ, פלדה או בטון - כאשר לכל אחד מהם מאפייני חוזק ומתח ייחודיים. ערכו יהיה תלוי בחומר הנבחר ובשימוש המיועד של המבנה.
 
 לאחר מכן, ציירו דיאגרמות של כוח גזירה ומומנט כיפוף כדי להמחיש את חלוקת העומס ולזהות נקודות מתח כיפוף מקסימליות. הדמיה זו היא המפתח למיטוב מימדי הקורה כדי למקסם את הבטיחות והיעילות של הקורה.
 
 לבסוף, חשבו את מודול החתך המינימלי שיאפשר לקורה להתנגד ללחץ כיפוף. מודולים גבוהים יותר מצביעים על התנגדות גדולה יותר. עבור קורות עץ, המעצב מציין יחס צורת חתך רוחב שיפיק את המודול הרצוי. עבור קורות פלדה, המעצב בוחר מקטעים קיימים, ומבטיח שהמודול של הקורה עובר את המינימום המחושב. בחירה זו מבטיחה שהקורה יכולה לעמוד בכוחות כיפוף, תוך שמירה על בטיחות ויציבות מבנית.
 
 גישה שיטתית זו משלבת שיקולי בטיחות עם ניתוח חומרים ועומסים, ומבטיחה שהקורה הנבחרת תשמור על שלמות המבנה ומהימנותו בעומסים צפויים, ובסופו של דבר מבטיחה ביצועים מבניים לטווח ארוך.
 
</div>

תהליך התכנון של קורות פריזמטיות הנתונות לכיפוף מתחיל בקביעת הלחץ המותר לחומר הנבחר.
הלחץ המותר הוא ...

Education

JoVE Core

Mechanical Engineering

הנדסת מכונות

Unit 1

יחידה 1

Analysis and Design of Beams for Bending

ניתוח ותכנון קורות לכפיפה

KEY TERMS AND CONCEPTS

מונחי מפתח ומושגים

sizing beams for safe bending loads

Prismatic beams have a uniform cross-section, and their design focuses on safe bending under load. The goal is to keep stress within a level the material can handle while the structure stays strong and stable.

The first step is to find the allowable stress for the chosen material. Designers can use values from material property tables, or they can divide the material's ultimate strength by a safety factor. This safety factor helps account for uncertainty, and its value depends on the material and the intended use of the structure.

Timber, steel, and concrete each have different strength and stress behavior, so the design method depends on the material. After selecting the material, the designer plots shear force and bending moment diagrams. These diagrams show how the load is distributed and help locate the points where bending stress is highest.

The final step is to calculate the minimum section modulus needed to resist bending stress. A higher section modulus means greater resistance to bending. For timber beams, the designer chooses a cross-section shape ratio that gives the needed modulus. For steel beams, the designer selects a standard section whose modulus is at least as large as the calculated minimum. This process helps the beam carry bending forces safely and maintain structural integrity over time.

Sizing Beams for Safe Bending Loads

design of prismatic beams for bending

Prismatic beams have a uniform cross-section, and their design focuses on safe bending under load. The goal is to keep stress within a level the material can handle while the structure stays strong and stable. The first step is to find the allowable stress for the chosen material. Designers can use values from material property tables, or they can divide the material's ultimate strength by a safety factor. This safety factor helps account for uncertainty, and its value depends on the material...

prismatic beams: problem solving

Timber Beam Design Under Distributed Load

Timber beam design under a distributed load uses the beam’s size and the wood’s properties to keep the structure safe. The beam’s length and width are known at the start. The timber’s grade and species also matter because they affect the allowable stress, which is the highest stress the material can safely handle. The first step is to treat the beam as a free body. A free-body diagram shows the forces and moments acting on the beam. From this, the support reactions can be found by balancing...

singularity functions for shear

Beam Shear Diagrams with Macaulay Brackets

Beam shear diagrams can be written with singularity functions when the load changes suddenly along the beam. In structural analysis, these functions help show discontinuous shear force with one mathematical expression, even when the loading is complex. They make it easier to describe how shear changes from one point to the next. The method starts with a free-body diagram of the beam. Then the beam is cut at specific points to check the shear force in each section. For a beam with width W and...

singularity functions for bending moment

Beam Load Modeling with Singularity Functions

Singularity functions help model beam loads and bending moments when the loading changes along the beam. They make it possible to write the bending moment with one mathematical expression instead of separate equations for each section. In this method, Macaulay’s brackets are often used to show where a load starts or stops. For a simply supported beam AB, the load is uniform from the midpoint M to the right support B. To find the bending moment, the beam is cut at different points. A cut...

key terms and concepts

Learn how prismatic beams are sized for bending by finding allowable stress, using shear and moment diagrams, and choosing the right section modulus.

Sizing Beams for Safe Bending Loads | JoVE K12

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Sizing Beams for Safe Bending Loads

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